1. Field of the Invention
This invention concerns an interferometer which analyzes wavefronts by the fringe scan method, and in particular concerns an interferometer which accurately measures the displacement of a reference mirror.
2. Description of the Prior Art
One method of measuring the shape of an object at wavelengths below the order of the wavelength of light, is the fringe scan method using an interferometer. In the fringe scan method, a light beam from a single source is split into two components, and reflected by a surface to be measured and a reference surface. The two reflected beams are combined so as to generate interference fringes on the image pickup surface of a CCD camera. Either the surface to be measured or the reference surface is displaced in the direction of the optic axis, the variation in the amount of light in each picture element of the camera is analyzed, and the shape of the surface to be measured is then determined.
To displace the surfaces along the optic axis, a piezo device or other phase shift device is used. Since the precision of the measurement is determined by the precision of the displacement, the piezo device must be accurately controlled.
In conventional interference systems, the response of the piezo device was considered as a function of the applied voltage. First, the system was calibrated to determine the relation between the response and the applied voltage, and the displacement of the reference surface was then computed from the applied voltage.
The response of the piezo device however varies not only due to the applied voltage, but also due to external disturbances such as temperature variations and/or vibration. If the displacement of the reference surface is computed based only on the applied voltage as described hereintofore, therefore, the measurement precision decreases.
The following three conventional methods of precisely measuring the response of the piezo device are known.
The first is disclosed in Preview Papers of the Applied Physics Academy No. 777, page 29a-ZE-3, published in Autumn 1989. According to this method, Young's interference patterns are formed on part of the interference surface to apply a shifter correction, and a phase shift is measured in real time by computing the phases of these patterns.
The second is a method disclosed in APPLIED OPTICS Vol. 22, No. 21, According to equations (9) and (10) given on page 3424 of this reference, the response of a piezo device can be measured by an ordinary digital interferometer system.
The third is disclosed in Riken Symposium Abstract 87-14. In "The Generation of Equidistant Interference Fringes and their Application" described in pages 31-34 of this reference, the phase of equidistant linear interference fringes is calculated by applying an inverse tangent of Fourier integration. This can then be used to measure the displacement of a peizo device with a polarizing interferometer, and measure the retardation of a phase shifter.
The above methods are however associated with the following disadvantages.
In the first method, in addition to the parts comprising the interferometer, special parts are required to detect the phase shift of a monitor mirror, etc. The diameter of the optical system is unnecessarily large because it comprises both a monitor and a sampler. Further, since the monitor and sampler are separate, their phase shifts may differ especially if there is a plurality of phase shift devices.
In the second method, it is assumed that the piezo device has a linear response, and a precise measurement cannot therefore be made if the response is non-linear. In general, piezo devices possess some non-linearity.
Ill the third method, as can be understood from equations (2), (3), (4) (which are expressed below in the specification) which form the principle of the measurement, the spatial frequency of the fringes must be accurately set. If the number of interference fringes slightly differs from this setting, the precision of the measurement decreases markedly. Further, special devices such as a birefringence prism must be used which makes the apparatus complex.